1. Field of the Invention
The present invention relates to an improvement of property variations and temperature dependency because of passive elements in an active filter circuit comprised of semiconductor integrated circuits.
FIG. 13 is a circuit diagram showing an embodiment of an active filter circuit which is a conventional primary lowpass filter.
Referring to FIG. 13, an input terminal 2 is connected to a base of an NPN transistor 13. A signal of dc bias voltage applied by a voltage source 4 superposed with an ac signal V.sub.i superposed is input to the input terminal 2.
The NPN transistor 13 has its collector connected to a power source 1 and its emitter connected through a resistor 15 (resistance value R.sub.E) to a first terminal of a constant current source 17. A second terminal of the constant current source 17 is grounded. The constant current source 17 generates dc current 2I.sub.3.
The constant current source 17 has its first terminal connected to a first terminal of a resistor 16 (resistance value R.sub.E). of which second terminal is connected to an emitter of an NPN transistor 14. The NPN transistor 14 has its base connected to an output terminal 24 and its collector connected to respective emitters of NPN transistors 18 and 19. The NPN transistor 18 has its collector connected to the power source 1 and its base connected to an emitter of an NPN transistor 7. The NPN transistor 19 has its collector connected to a first terminal of a constant current source 20, of which second terminal is connected to the power source 1. The collector of the NPN transistor 19 is also connected to a base of an NPN transistor 22 and a first terminal of a capacitor 21 (capacity C.sub.1). A second terminal of the capacitor 21 is grounded.
An NPN transistor 22 has its collector connected to the power source 1 and its emitter connected to an output terminal 24 and a first terminal of a constant current source 23, of which second terminal is grounded. The NPN transistor 19 has its base connected to an emitter of an NPN transistor 6, while the NPN transistors 6 and 7 have their respective bases and collectors connected in common to a voltage source 5. The NPN transistor 6 has its emitter connected to a collector of an NPN transistor 9 while the NPN transistor 7 has its emitter connected to a collector of an NPN transistor 10. An emitter of the NPN transistor 9 is grounded through a resistor 11 (resistance value R.sub.1) while an emitter of the NPN transistor 10 is grounded through a resistor 12 (resistance value R.sub.2). The NPN transistors 9 and 10 have their respective bases connected in common to a voltage source 8.
In general, emitter current I.sub.E in transistors can be expressed as follows: ##EQU1## where V.sub.BE is a base-emitter voltage, k is a Boltzmann's constant, T is an ambient temperature of transistors which are expressed by an absolute temperature, and q is an amount of electric charge of electrons. According to the formula 1, an emitter resistor r.sub.e of the transistors 13 and 14 can be expressed as follows: ##EQU2##
Thus, utilizing the ac signal V.sub.i input to the input terminal 2 and an ac signal V.sub.o appearing at an output terminal, an ac component I.sub.14C of the collector current in the transistor 14 can be expressed as follows: ##EQU3##
An ac component I.sub.19C of the collector current in the transistor 19 is determined by emitter currents I.sub.6E and I.sub.7E as follows: ##EQU4##
A value of the dc current from the current source 20 is set equal to that of the dc component of the collector current in the transistor 19.
An ac voltage V.sub.22B applied to a base of the transistor 22 can be expressed as follows: ##EQU5## where f is a frequency of the signal V.sub.i and .pi. is a ratio of the circumference of a circle to its diameter.
The ac signal V.sub.o appearing in the output terminal 24 is equal to the ac voltage V.sub.22B, and hence it can be expressed as follows: ##EQU6##
The formulae (2), (3), (4) and (6) together lead the following formula: ##EQU7##
I.sub.6E and I.sub.7E are determined by voltage V.sub.8 of a voltage source 8 and resistance values R.sub.1 and R.sub.2, and they can be expressed as follows: ##EQU8##
V.sub.BE9 and V.sub.BE10 are base-emitter voltages in the transistors 9 and 10.
A frequency characteristic of the dc signal V.sub.o output at the output terminal 24 is, as will be recognized in the formula 7, determined by the capacity C.sub.1 of the capacitor 21 built in an semiconductor integrated circuit, the resistance value R.sub.E of the built-in resistors 15 and 16, the current I.sub.3, the absolute temperature T, and the ratio of the emitted current I.sub.6E to the emitter current I.sub.7E within the integrated circuit.
A conventional active filter circuit is configured as mentioned above, and therefore, its frequency characteristic depends upon a capacity of a capacitor build in a semiconductor integrated circuit, a resistance value of built-in resistors and an absolute temperature. Thus, there is the disadvantage that variations in manufacturing semiconductor integrated circuits cause variations in capacity, resistance value and ambient temperature to change their characteristics.